This research uses mathematical and computational techniques to determine the functional properties of local-circuit neurons, based on the well-founded results of cable theory, compartmental analysis, and biophysics of ionic fluxes across nerve-cell membranes. Five specific problem areas are addressed: (1) interaction of chemical and electrical synapses in neuronal circuits, (2) integrative properties of nonspiking neurons, (3) dynamics of reciprocal synapses, (4) functional roles of dendritic spines, and (5) properties of neurons exhibiting dendritic spikes. The aim of the studies is to provide realistic, quantitative, and consistent data for the behavior of these systems, so that both experimental and theoretical investigations can be rigorously based on solid theory, rather than on qualitative estimates.